Answer:
1. a) x1 = -8 y x2 = -4
b) x1 = -1/3
2. a) x1 = 0 y x2 = -5
b) x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) x1 = 3, x2 = -3 las otras dos raices son complejas.
Step-by-step explanation:
1. a) [tex]x^{2}+12x+32=0[/tex]
Factorizando:
[tex](x+8)(x+4)=0[/tex]
Entonces: x1 = -8 y x2 = -4
4. a) x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]9x^{2}+6x+1=0[/tex]
Factorizando:
[tex](3x+1)(3x+1)=0[/tex]
[tex](3x+1)^{2}=0[/tex]
Entonces: x1 = -1/3
2. a) [tex]2x^{2}+5x=0[/tex]
Aplicando factor comun:
[tex]x(x+5)=0[/tex]
Entonces: x1 = 0 y x2 = -5
b) [tex]2x^{2}-32=0[/tex]
Despejamos x.
[tex]2x^{2}=32[/tex]
[tex]x^{2}=16[/tex]
Entonces: x1 = 4 y x2 = -4
3. m debe ser 6. Asi tendriamos (x+3)²=0
4. a) [tex]x^{4}-25x^{2}+144=0[/tex]
Hacemos cambio de variable: [tex]w=x^{2}[/tex]
[tex]w^{2}-25w+144=0[/tex]
Ahara podemos factorizar:
[tex](w-16)(w-9)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-16)(x^{2}-9)=0[/tex]
Entonces los valores de x son: x1 = 4, x2 = -4, x3 = 3 y x3 = -3
b) [tex]x^{4}+9x^{2}-162=0[/tex]
Hacemos cambio de variable: [tex]z=x^{2}[/tex]
[tex]z^{2}+9z-162=0[/tex]
Ahara podemos factorizar:
[tex](z-9)(z+18)=0[/tex]
Usando el cambio de variable nuevamente.
[tex](x^{2}-9)(x^{2}+18)=0[/tex]
Entonces los valores de x son: x1 = 3, x2 = -3 las otras dos raices son complejas.
Espero ye haya servido!
Hey plz could you help me with this???? Tysm
Answer:
25.71
Step-by-step explanation:
πr + d
3.142(5) + 10
= 25.71
i think
What type of line is PQ¯¯¯¯¯¯¯¯?
A. median
B. angle bisector
C. side bisector
D. altitude
Answer:
angle bisector
Step-by-step explanation:
Since the line divided the top angle into two equal pieces we call this an angle bisector.
Find the distance between the points (2, 4) and (8, -8) on a coordinate plane, to the nearest whole number.
A.7
B.11
C.13
D.16
Answer:
C
Step-by-step explanation:
distance between two points formula:
[tex]d = \sqrt{( x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]
where the x and y values are derived from the known points
we are given the points (2, 4) and (8, -8)
given these two points let's define each variable
x1 = 2
x2 = 8
y1 = 4
y2 = -8
we now substitute in these values into the formula
[tex]d = \sqrt{(8 - 2) ^{2} + ( - 8 - 4)^{2} } [/tex]
now we evaluate the expression using PEMDAS
first we do the subtraction inside of the parenthesis
8 - 2 = 6
-8 - 4 = -12
d = sqrt(6)^2 + (-12)^2
next we do the exponents
6^2 = 36
-12^2 = 144
d = sqrt( 144 + 36 )
next do the addition inside of the parenthesis
144 + 36 = 180
d = sqrt ( 180 )
finally we do the square root of 180
sqrt ( 180 ) = 13 ( rounded to the nearest whole )
d = 13
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
https://brainly.com/question/22213822
in a group of 300 mice, 75% are male and 20% are albino. What is the greatest number of mice in the group that could be both female and not albino?
a) 45
b)60
c)75
d)225
Draw the image of ABC under a dilation whose center is P and scale factor is 1/3
A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:
AC = 6.7/3 = 2.2
AB = 12.4/3 = 4.1
CB = 12.7/3 = 4.2
Read more on dilation here: brainly.com/question/20482938
#SPJ1
what is the formula to calculate VAT percentage
Answer:
Take the gross amount of any sum (items you sell or buy) – that is, the total including any VAT – and divide it by 117.5, if the VAT rate is 17.5 per cent. (If the rate is different, add 100 to the VAT percentage rate and divide by that number.)
Answer:
divide by 117.5 if the rate different, add 100 to the percentage and divide by the number therefore multiply by 100 to get the total
Step-by-step explanation:
the formula to calculate vat percentage
the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
Anual is a word-processor operator. He makes N$12, 50 an hour. Determine his earnings for a week if he works for 48 hours.
Answer: $600
Step-by-step explanation:
Given
Anual makes [tex]\$12.50[/tex] an hour
For 48 hours, he makes
[tex]\Rightarrow 48\times 12.5\\\Rightarrow \$600[/tex]
Thus, he will make $600 for 48 hours
PLEASE HELP solve step by step
Answer:
-3y/x^2
Step-by-step explanation:
-5/15 = -3
When dividing variables with powers, subtract the powers.
x^2 - x^4 = x^-2
y^3 - y^2 = y
z^4 - z^4 = 0
therefore we have -3 x^-2 y
Since we can't have negative powers, divide (move the x^-2 to the bottom and make positive)
-3y / x^2
Hope this helps! Let me know if I am wrong ^w^
Answer:
- y/3x^2
Step-by-step explanation:
The negative sign goes between y and 3x^2
Find the angles of 22 and 24 thanks
Answer:
22) 119
24) 15
Step-by-step explanation:
22) 61 + b = 180 <-- supplementary because on the same line
b = 119 <-- subtracted 61 from both sides
24) 87 + (6x + 3) = 180 <-- supplementary because on the same line
87 + 6x + 3 = 180 <-- take out parantheses
90 + 6x = 180 <-- add like terms
6x = 90 <-- subtracted 90 from both sides
x = 15 <-- solve for x by dividing 6 from both sides
a bag contains 10 white balls and 14 red balls.a ball is taken out of the bag,what is the probability that it is a red ball
Answer:
7/12
Step-by-step explanation:
10 white balls and 14 red balls = 24 balls
P( red) = number of red balls / total balls
=14/24
=7/12
The perimeter of a rectangular garden is 4534 m. The length is 1125 m more than thrice the width. Find the length and the width of the rectangular garden. (Estimate to the nearest tenths place and verify the reasonableness).
Answer:
length = 1696 m
breadth = 571 m
Step-by-step explanation:
perimeter = 4534 m
let breadth be b
so length = b + 1125 m
so
perimeter of rectangular garden = 2(l+b)
4534 m = 2(b+1125m+b) {substituting the value}
or, 4534 m = 2(2b+1125m)
or, 4534 m = 4b + 2250 m
or, 4534 m - 2250m = 4b
or, 2284m = 4b
or, b = 2284m/4
so, b = 571m
so, l = b + 1125 m
= 571 m + 1125m
= 1696 m
What is the solution to the inequality?
-x/4 < 6
O A. x<-24
O B. x<-2
O C. x>-24
O D. x>-2
Answer:
x > -24
Step-by-step explanation:
-x/4 < 6
Multiply each side by -4, remembering to flip the inequality
-x/4 *-4> 6*-4
x > -24
[tex]\boxed{\large{\bold{\red{ANSWER~:) }}}}[/tex]
x>-24Step-by-step explanation:[tex]\sf{\dfrac{-x}{4}<6 }[/tex] [tex]\sf{\dfrac{-x}{4}×(-4)>6×(-4) }[/tex] [tex]\sf{ x>-24 }[/tex][tex]\bold{ Note - }[/tex]
By multiply negetive number,we need to change the side of the inequality.Can someone help me with this math homework please!
Answer:
D
Step-by-step explanation:
The line is decreasing. Option B is wrong because if it was true, it means that the entire candle burns in an hour
Jimmy, who is five and a half feet tall, sees a bird at the top of a tree and wonders how tall the tree is. Jimmy stands 18 feet from the tree. Jimmy takes an inclinometer (a device used to calculate angles of elevation) and measures the angle created from his horizontal gaze and the bird to be 50 degrees. How tall is the tree?
Answer:
100
Step-by-step explanation:
it is 50 when he sees it in a horizontal line so double it to see how much it is if it where straight
Find the perimeter of \triangle SOW△SOWtriangle, S, O, W.
If entering your answer as a decimal, round your final answer to the nearest hundredth.
Answer:
the perimeter is 30 units
Which of the following is a point-slope equation for a line with the point (-2, 4) and a slope of 3?
Answer:
y=3x+10
Step-by-step explanation:
y-4=(x+2)3
y-4=3x+6
y =3x+10
sipho made a 12.5% when he sold a coat for E437.50 .calculate original cost of the coat
Answer:
E500
Step-by-step explanation:
Given x the original price of the coat
437.5 + 0.125x = x
437.5 = 0.875x
x = E500
Find the missing length indicated
Answer:
x =1 08
Step-by-step explanation:
Study the diagram of circle C, where two chords, AB¯¯¯¯¯¯¯¯ and DE¯¯¯¯¯¯¯¯, are equidistant from the center.
The diagram as described in the problem.
If AB=3x−7, and DE=5(x−5), what is the length of AB¯¯¯¯¯¯¯¯?
Enter the correct value.
Answer:
Step-by-step explanation:
If AB and DE are equidistant from the center, that means that they are the same length. We set the equations equal to one another and solve for x:
3x - 7 = 5(x - 5) and
3x - 7 = 5x - 25 and
18 = 2x so
x = 9. Now we sub that into the expression for AB (or DE since they're the same length):
3(9) - 7 = 20
Both AB and DE measure 20 units.
Can someone help me out
Answer:
60
Step-by-step explanation:
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
In a test containing 10 questions, (+5) marks are awarded for every correct answer, (-1) mark for every incorrect answer and 0 for not attempting the questions. If Rashid gets 4 correct answers and 6 incorrect answers, what is his score?
Answer:
14
Step-by-step explanation:
10 questions = 4 correct + 6 incorrect
4 correct = 4* 5 = 20
6 incorrect = 6* (-1) = -6
His score is 20 -6 = 14 points
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
Which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2?
Answer:
y=x-2,
so'n
y-x=2 answer you haven't write value.
The reliability coefficient of scores in an end of semester examination. If the variance of the exam score is 100. What is the standard error of measurement ?
Answer:
I Will explained you youuuuuu<uuuuuuuuuu
Ben is 4 times as old as Ishaan. 6 years ago, Ben was 6 times as old as Ishaan.
How old is Ishaan now?
Answer:
Ishaan is currently 15 years old.
Step-by-step explanation:
Let B represent Ben's current age and I represent Ishann's current age.
Ben is four times as old as Ishaan. In other words:
[tex]B=4I[/tex]
Six years ago, Ben was six times as old as Ishaan. In other words:
[tex]B-6=6(I-6)[/tex]
Solve for I. Substitute:
[tex](4I)-6=6(I-6)[/tex]
Distribute:
[tex]4I-6=6I-36[/tex]
Subtract 4I from both sides and add 36 to both sides:
[tex]2I=30[/tex]
And divide both sides by two. Hence:
[tex]I=15[/tex]
Ishaan is currently 15 years old.
Answer:
Age of Ishaan = 15 years
Step-by-step explanation:
Let Ishaan's age = x years
Age of Ben = 4 * x = 4x years
6Years ago:
Age of Ishaan = x - 6
Age of Ben = 4x - 6
6 years ago, Ben was 6 times as old as Ishaan
So, Age of Ben = 6 * Ishaan's age
4x - 6 = 6 *(x-6)
4x - 6 = 6x - 36
Add 36 to both sides
4x - 6 + 36 = 6x
4x + 30 = 6x
Subtract '4x' from both sides
30 = 6x - 4x
30 = 2x
2x = 30
Divide both by 2 sides
x = 30/2
x = 15
The graph of g(x) is a translation of the function f(x)=x^2. The vertex of g(x) Is located 5units above and 7 units to the right of the vertex of f(x). Which equation represents g(x)
Step-by-step explanation:
The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.
Use the comparison test to determine if the series is convergent or divergent. 6/3+6/9+6/27+...
a. convergent
b. divergent
